Hey Martin,
every relay has a control input which is the coil that activates the relay switches, and a number of one or more switches that are switched by powering the control coil on or off.
The flyback diode is any diode connected across an inductor (= the relay’s control coil) used to eliminate flyback, which is the sudden voltage spike seen across an inductive load when its supply current is suddenly reduced or interrupted. A diode’s schematic diagram looks like this:
Do you see the diode above in the diagram from the VFD manual? It is wired in parallel to the relay control coil (RY). You can recognize the cathode pin on a diode by a color band printed on that side of the diode housing. The diode is wired parallel to the relay’s control coil, and its anode goes to pin 11 or 12 (the open collector output) and the cathode goes to positive output of your DC power supply. The negative output of your DC power supply goes to CM2.
Yes, on an open collector output, you need a power supply because the open collector does not provide any voltage. The VFD has some 24 V output, but this is just a positive logic voltage for the control inputs, I would not use it to drive a relay. Using an external 24 V power supply like the Meanwell MDR or similar which attaches to a DIN rail that you usually have in your control cabinet is usual when using relays on open collector outputs. 24 DC is also used by other devices like the safety relay Omron G9SE (datasheet). Depending on the maximum current that are allowed for the open collector output and for the relay, you would also possibly need a pull-up resistor to limit the current.
I would use a general purpose diode, e.g. 1N400x.
PS: I remember that the other day I posted a circuit diagram:
It has an additional manual switch for using the dust collector on other power tools like circular saw while the VFD can switch it on and off automatically (by the CNC) at the same time.
The relay switches both power wires (N and L) on and off which is more safe but of course you can also switch only one wire to the dust collector on and off by a SPST relay.